On ψH(.)-operator in weak structure spaces with hereditary classes

Weak structure space (briefly, wss ) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce ψ H ( . ) -operator in heredi...

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Bibliographic Details
Published in:Journal of the Egyptian Mathematical Society 2020-12, Vol.28 (1)
Main Authors: Abu-Donia, H. M., Hosny, Rodyna A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Research
Online Access:Get full text
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Summary:Weak structure space (briefly, wss ) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce ψ H ( . ) -operator in hereditary class weak structure space (briefly, H w s s ) ( X , w , H ) and examine a number of its characteristics. Additionally, we clarify some relations that are credible in topological spaces but cannot be realized in generalized ones. As a generalization of w -open sets and w -semiopen sets, certain new kind of sets in a weak structure space via ψ H ( . ) -operator called ψ H -semiopen sets are introduced. We prove that the family of ψ H -semiopen sets composes a supra-topology on X . In view of hereditary class H 0 , w T 1 -axiom is formulated and also some of their features are investigated.
ISSN:1110-256X
2090-9128
DOI:10.1186/s42787-020-00107-2